Polyelectrolyte charge

The effects of ion valence and polyelectrolyte charge density showed that at very low ionic strength found that when the counterion valence of added salt changes from monovalent (NaCl) to divalent (MgS04), the reduced viscosity decreases by a factor of about 4.5. If La(N03)3 is used, the reduced viscosity will be further decreased although not drastically. As for polyelectrolyte charge density, the intrinsic viscosity was found to increase with it because of an enhanced intrachain electrostatic repulsion (Antonietti et al. 1997). 

Phase II describes saturated counterion condensation [47]. The polyelectrolyte charge is nearly compensated by the counterions [47]. The uncondensed counterions are dispersed in a self-similar fashion throughout the cylindrical region [47]. In fact, the number of counterions bounded between radius r and, say, 2r is independent of r [47]. 

In the latter case the total interaction, which is what can be measured, is affected by the net charge of the surface and the adsorbed layer, ion-ion correlations, bridging interactions and steric confinement of the polymer chain [116]. We note that polyelectrolytes are often present as additives in colloidal dispersions and the character of the forces generated by the polyelectrolyte adsorption layers has a paramount influence on stability of these colloidal systems. With the aim to illustrate what can be learnt about polyelectrolyte adsorption layers using the SFA, we will look at the influence of the polyelectrolyte charge density on the forces acting between surfaces coated with polyelectroytes. We will consider an example where the polyelectrolyte charge density is varied by a systematic... 

There is a range of parameters other than polyelectrolyte charge density that has an important influence on the generated surface interactions, for instance, counterion valency and ionic strength of solution [121-123], the order of addition of polyelectrolyte and salt [124], polyelectrolyte concentration [125], presence of surfactants [31, 119, 126], and finally, the chemical structure of the polyelectrolyte itself [127]. A rich literature is available on these topics (see Ref. [115] and references therein). 

Electrostatic free energy of interaction between the polyelectrolyte charges and the ionic atmosphere of loosely bound counterions. 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

Figure 5.40 shows an experimental corroboration of the Importance of charge compensation. The figure gives the ratio between the adsorbed polyelectrolyte charge and the surface charge (defined by 9 = as a... 

Figure S.40. Charge due to adsorbed polyelectrolyte per unit of surface charge (Sa s) as a function of the total (added) amount of polyelectrolyte charge per unit surface charge (9 ). for cationic polyacrylamides of different molecular weights (expressed in K 3 kg/mole) (a) and of different polymer charge densities (b) adsorbed from salt-free solutions on anionic polyst3TFene latex. Redrawn from ref.

For polyelectrolytes (charged polymers), a plot of rjgp/c versus c may be a curve. An alternate expression of Fuoss and Strauss (1948) can be used (Chamberlain and Rao, 2000) ... 

For polyelectrolytes (charged polymers), Tam and Hu (1993) utilized the expression for specific viscosity in the equation of Fuoss-Strauss ... 

The set of results presented here allows us to understand better the properties of polyelectrolytes in the presence of multivalent counterions. However, these systems are very complex, and we hope that future experimental and theoretical work will permit us to progress significantly. We must keep in mind that while polyelectrolytes and multivalent counterion systems are interesting from a fundamental point of view, they are also of practical interest, as for instance in the biological field and in depollution process. An extension to polyelectrolyte/charged colloid systems that present some complex phase diagrams is in progress. 

FIG. 11 Attachment barrier for a polyelectrolyte (charge density zp = —1), approaching an (initially) uncharged surface. The curves are calculated for several degrees of polymer coverage ffq, i.e., for different stages in the adsorption process. (Calculations by Hoogendam [14].)... 

A dependence of the hydrodynamic layer thickness on the polyelectrolyte charge density is followed in [15] for polyacrylamides with degrees of hydrolysis 3.4, 9.8, and 19.1%, adsorbed on /3-FeOOH particles. Equal values of Lr = 6 nm are found by electro-optics irrespective of the polymer charge (Table 1), although the theoretical prediction for this dependence is quite different. 

A decrease of the adsorbed HPAM amounts with increasing charge density is determined in this case by radioactive measurements. This is consistent with the theoretical predictions of Evers et al. [106] and their next extension by Bohmer et al. [61]. Such a decrease has been experimentally shown also in Refs. 95, 107, and 108. The thickness of the adsorbed layer for a 100% charged polyelectrolyte is found, for instance, to be 1 nm and about 3-4 nm for the 30% charged one (this volume, chapter by Claesson). The reduction in polyelectrolyte charge density to 10% results in an increase in the adsorbed layer thickness to 10-20 nm. 

In combination with adsorption measurements, electro-optics is proved to be a powerful technique for studying the structure of adsorbed polyelectrolyte layers. Our data show flat conformation of the adsorbed macromolecules, which slightly depends on the polyelectrolyte charge density in accordance with the theory for weak poly electrolytes. Counterion condensation is also suggested on the surface of weakly charged poly electrolytes, which has not been predicted from the theory. 

Zhu, Y., Sun, Y. (2004). The influence of polyelectrolyte charges of polyurethane membrane surface on the growth of human endothelial cells. Colloids Surf. B Biointerfaces. 36.49-55. 

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